Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

using namespace std;

#define N 300000

int n,T,p[N];

bool cyc(int x,int y,int z){
	return (p[x]<p[y]&&p[y]<p[z])||(p[y]<p[z]&&p[z]<p[x])||(p[z]<p[x]&&p[x]<p[y]);
}

int main(){
	scanf("%d",&n);
	for (int i=1;i<=n;++i){
		int x; scanf("%d",&x);
		p[x]=i;
	}
	p[n+1]=n+1;
	T=0;
	for (int i=n,f=0;i;--i){
		if (T==0){
			if (p[i]>p[i+1]){++T; f=i+1;}
		}
		else{
			if (!cyc(f,i,i+1)){++T; f=i+1;}
		}
	}
	printf("%d\n",T);
	
	return 0;
}